Final answer:
The coronary vessel that resides in the coronary sulcus is the right coronary artery. It is responsible for distributing blood to the right atrium, parts of both ventricles, and the heart's conduction system, and gives rise to the posterior interventricular artery.
Step-by-step explanation:
A specific coronary vessel that lies in the coronary sulcus is the right coronary artery.
The right coronary artery travels along the coronary sulcus and serves multiple important functions. It supplies blood to the right atrium, to parts of both ventricles, and to the heart's conduction system. From the right coronary artery, the posterior interventricular artery, also known as the posterior descending artery, branches off and runs along the posterior portion of the interventricular sulcus, reaching toward the heart's apex.
This artery provides blood to the interventricular septum and portions of the ventricles. Conversely, the small cardiac vein, which also parallels the right coronary artery, is not an artery but a vein that drains the posterior surfaces of the right atrium and ventricle into the coronary sinus.